In the multi-stage secret sharing scheme, the participants of authorized sets in each level of access structures can jointly reconstruct the corresponding secret. But in reality, adversaries who corrupted an unauthorized set can obtain some or even all of the share information of the uncorrupted participants through memory attacks, thereby illegally obtaining some or even all of the shared secrets. Facing with such memory leaks, the existing multi-stage secret sharing schemes are no longer secure. Based on this, this study firstly proposes a formal computational security model of indistinguishable ability against chosen secret attack for multi-stage secret sharing. Then, using the combination of the physical unclonable function and the fuzzy extractor, a verifiable memory leakage-resistant multi- stage secret sharing scheme for general access structures is constructed based on the minimal linear codes. Furthermore, in the presence of a memory attacker, it is proved that the scheme is computational secure in the random oracle model. Finally, the proposed scheme is compared with the existing schemes in terms of their properties and computational complexity.